Also on Sunday, fourth-placed Real Sociedad will hope to extend their remarkable record of one defeat in 18 league games when they go to Espanyol.
At the bottom, there is a six-way scrap to remain in the top flight.
And with Celta Vigo and Zaragoza drawing the top two it may provide a chink of light to the others.
Rock-bottom Deportivo La Coruna were given renewed hope by their win over Celta last time out and they have the chance to build on that victory when they visit third-bottom Real Mallorca.
Osasuna and Granada are the other clubs in trouble. Osasuna, in 16th, go to Real Valladolid and Granada visit Athletic on Monday.
Monday's other game sees Real Betis host Getafe.
Saturday's La Liga Round-Up
Lionel Messi again made history but his goal was not enough to earn Barcelona a win over relegation-threatened Celta Vigo as the teams shared a 2-2 draw.
The Argentina international is no stranger to treading new ground and his 73rd-minute goal on Saturday night meant he has scored in 19 successive La Liga matches.
In doing so he has found the net against every other side in the Spanish top flight - the first player to ever do that in consecutive matches - and he has 29 goals from his last 19.
Saturday night's would not be the winner, though, with Borja Oubina's late header earning Celta a point, with Naxto Insa's opener having been earlier scrubbed out by Cristian Tello's goal.
It was a good day for Barca, however, with Messi's latest record being set and Eric Abidal on the bench for the first time since a liver transplant over a year ago.
The France defender did not make it on to the field but his return is a significant one, as is that of coach Tito Vilanova who was not at the game but is back in the country after undergoing chemotherapy in America.
Second-placed Real Madrid missed the chance to make things slightly less comfortable for Barcelona as they were too were held by a team fighting the drop, fourth-bottom Real Zaragoza.
Madrid could have trimmed their arch rivals' lead to 11 points if they could beat Zaragoza and claim a seventh successive league victory.
However, like Barca, they had to settle for just a point with Rodri putting Zaragoza ahead early on before Cristiano Ronaldo levelled things up just before the break with his 28th La Liga goal of the campaign.
Neither side could go on to force a winner in the second half, with Marcelo hitting the post for Madrid and both goalkeepers making a number of vital interventions.
Malaga reclaimed fourth spot with a 3-1 victory at Rayo Vallecano.
Weligton gave Manuel Pellegrini's side the lead but Piti levelled for the hosts from the penalty spot.
Former Real Madrid forward Julio Baptista scored his first goal in 18 months to restore Malaga's lead early in the second half before Pedro Morales secured all three points with a wonderful goal.
In the evening's late game Levante won their first league match since January with a 1-0 home triumph over Sevilla.
Ruben struck the winner five minutes before half-time as Levante leap-frogged above Sevilla into 10th.
Saturday's La Liga Results
Sunday's La Liga Fixtures
Monday's La Liga Fixtures
Athletic Bilbao vs Granada
Real Betis vs Getafe